Self-stabilizing exchange-mediated spin transport

Long-range spin transport in magnetic systems can be achieved by means of exchange-mediated spin textures with robust topological winding, a phenomenon referred to as spin superfluidity. Its experimental signatures have been discussed in antiferromagnets, which are nearly free of dipolar interaction. However, in ferromagnets, which possess non-negligible dipole fields, realization of such spin transport has remained a challenge. Using micromagnetic simulations, we investigate coherent exchange-mediated spin transport in extended thin ferromagnetic films. We uncover a two-fluid state in which the long-range spin transport by spin textures coexists with spin waves, as well as a soliton-screened spin transport regime at high spin injection biases. Both states are associated with distinct spin texture reconstructions near the spin injection region and sustain spin transport over large distances.

Figure 1

EMS in the absence of dipolar interaction. (a) Schematic view of the thin film. The spin injector provides spin current with out-of-plane polarization (blue arrows). The spin sinks are shown. The red arrows represent a magnetization snapshot. (b) Initial EMS velocity (black circles) and base frequency (red circles) as functions of the current density. Three regimes of the EMS are marked. Black lines show transmitted spin current $\tau$ (in the same units as the EMS velocity) calculated based on the analytical model. Spatial dependence of the EMS velocity (c) in regime I, (d) in regime II at $j=3.1\times {10}^{11}$ A ${\mathrm{m}}^{-2}$, and (e) in regime III at $j=4.6\times {10}^{11}$ A ${\mathrm{m}}^{-2}$.

Figure 2

EMS in the presence of dipolar interaction. (a) Threshold current as a function of film thickness. (b) Initial EMS velocity and base frequency as functions of the current density for a 5-nm-thick film (subthreshold regime omitted for clarity). (c) Spatial dependence of the EMS velocity.

Figure 3

Perturbations of the magnetization spiral in the presence of dipolar interaction, a snapshot after 500 ns for $j=4\times {10}^{10}$ A ${\mathrm{m}}^{-2}$. (a) In-plane components of the normalized magnetization, $m_{\mathrm{x}}$ (blue solid line) and $m_{\mathrm{y}}$ (red solid line), deviate from the sinusoidal behavior. (b) The out-of-plane component $m_{\mathrm{z}}$ reveals peaks when $m_{\mathrm{x}}$ has an extremum. (c) The divergence of the magnetization is linked to the magnetostatic field.

Figure 4

Impact of the injector width on EMS. (a) Base frequency $\mathrm{\Omega }$ for different injector widths. (b) The first critical current density decreases as $\propto 1/w$ (red line), where $w$ is the injector width.